Dark Shadows when using AO with Transparent Materials?
There are several thing that could cause this, including


Shadows

Make sure that the table material has Receive Transparent enabled:  



With Receive Transparent and Without Receive Transparent: 




As you can see form this render with the glass raised, the reason for this is that even if the glass casts a transparent shadow, unless Receive Transparent is enabled for the table, solid black shadow is rendered which the glass then refracts:

Ambient Occlusion:
Ambient Occlusion would cause this too, as it works by darkening surfaces that are close to other objects. (The closer the darker)
Then you have the same problem as Receive Transparent, with the glass refracting the dark areas.

Add blend mode:



Multiply blend mode, with the glass on the table and with it in the air:




To make this disappear, you can enable Indirect Lighting in Properties > World

However, this can get your rendertimes rather insane, (Just for this low resolution render it took 2:27.26)


And as already mentioned by SteveW:


Depth
The Depth setting from one to four:




And at a value of 20 :



Cycles

Probably the best way to do this is use Cycles, as you need caustics to get light to properly illuminate after being refracted through the glass.

(quick example:)